Looks like Europcar has an office at the railway station in Würzburg, an hour's ride by regional train from Rothenburg. The fare from Würzburg to Rothenburg is €11,50 pP 2nd cl.
Accoding to Europcar, there is also a drop off in Ansbach (don't know the open times), 38-49 min from Rothenburg ob der Tauber Bhf. A VGN TagesTicket Plus, available at the Ansbach station automat for €12,50, will cover both of you from Ansbach to Rothenburg.
You do know that when you drive towards the Alps you will be driving away from Rothenburg. With a Bayern-Ticket, you could take the train in the morning to Garmisch-Partenkirchen, have lunch, then take trains (less than 5 hours) back via Munich to Rothenburg, all for €28 for both of you.